Factor the trinomial by $-1$ for an easier handling

Factor the trinomial $-\left(x^2-7x+10\right)$ finding two numbers that multiply to form $10$ and added form $-7$

Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values

Factor the trinomial $\left(x^2-7x+10\right)$ finding two numbers that multiply to form $10$ and added form $-7$

Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values

Multiply both sides of the equation by $-1$

Break the equation in $2$ factors and set each factor equal to zero, to obtain simpler equations

Solve the equation ($1$)

We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $-2$ from both sides of the equation

Canceling terms on both sides

Solve the equation ($2$)

We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $-5$ from both sides of the equation

Canceling terms on both sides

Combining all solutions, the $2$ solutions of the equation are